Lens system for a copying machine

ABSTRACT

A three group, three component lens system comprising, in order from one side a first, positive meniscus lens defining a convex surface directed to an object, a second, biconcave lens, and a third, biconvex lens. At least one of the three lenses is formed of plastic. It is recommended to satisfy the following conditional expression: 
     
         0.1 f&lt;f1+f2&lt;0.2f 
    
     where f is a focal length of the entire lens system, f1 is a focal length of said first lens, and f2 is a focal length of said second lens.

This is a continuation of application Ser. No. 07/499,096, filed on Mar.26, 1990, for a LENS SYSTEM FOR A COPYING MACHINE, now abandoned.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a compact three group, three component lenssystem for use in a copying machine.

2. Description of the Prior Art

Generally, the conventional lens system used in a copying machine or thelike includes four to six lenses. Further, the lens system of a copyingmachine or the like usually is used in a realsize range, and comprises asymmetric type lens system for avoiding distortion, aberration and thelike.

With the copying machine becoming compact in recent years, there havebeen increasing demands for the lens system used therein to be compact,lightweight and low cost. Thus, a lens system having excellentperformance with a reduced number of lenses is desired.

To date, however, a three component lens system for use in a copyingmachine has been non-existent.

SUMMARY OF THE INVENTION

An object of this invention is to provide a lens system for use in acopying machine, which has a reduced number of lenses to realize lowcost, compactness and excellent performance.

The above object is fulfilled, according to this invention, by a threegroup, three component lens system comprising, in order from one side, afirst, positive meniscus lens defining a convex surface directed to anobject, a second lens having a negative power, and a third lens having apositive power, wherein at least one of the three lenses is formed ofplastic.

In another aspect of this invention, the above object is fulfilled by athree group, three component lens system comprising, in order from oneside, a first positive meniscus lens defining a convex surface directedto an object, a second, biconcave lens, and a third, biconvex lens,wherein at least one of the three lenses is formed of plastic. In eachof the lens systems noted above, one of the three lenses is formed ofplastic to realize low cost and lightness. These lens systems arecomparable to or exceed the conventional lens systems in performance.Further, the lens systems of this invention are compact with a reducedtotal length, which contributes toward compactness of an entire copyingmachine.

The foregoing and other objects, features and advantages of theinvention will be apparent from the following more particulardescription of preferred embodiments of the invention, as illustrated inthe accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a sectional view of a lens system according to a firstembodiment of this invention.

FIGS. 2a, 2b, and 2c are showing aberration curves of the lens systemshown in FIG. 1,

FIG. 3 is a sectional view of a lens system according to a secondembodiment of this invention,

FIGS. 4a, 4b, and 4c are views showing aberration curves of the lenssystem shown in FIG. 3,

FIG. 5 is a sectional view of a lens system according to a thirdembodiment of this invention,

FIGS. 6a, 6b, and 6c are views showing aberration curves of the lenssystem shown in FIG. 5,

FIG. 7 is a sectional view of a lens system according to a fourthembodiment of this invention,

FIGS. 8a, 8b, 8c are views showing aberration curves of the lens systemshown in FIG. 7,

FIG. 9 is a sectional view of a lens system according to a fifthembodiment of this invention,

FIGS. 10a, 10b, 10c are sectional views showing aberration curves of thelens system shown in FIG. 9,

FIG. 11 is a sectional view of a lens system according to a sixthembodiment of this invention,

FIGS. 12a, 12b, and 12c are views showing aberration curves of the lenssystem shown in FIG. 11,

FIG. 13 is a sectional view of a lens system according to a seventhembodiment of this invention,

FIGS. 14a, 14b, and 14c are views showing aberration curves of the lenssystem shown in FIG. 13,

FIG. 15 is a sectional view of a lens system according to an eighthembodiment of this invention,

FIGS. 16a, 16b, and 16c are views showing aberration curves of the lenssystem shown in FIG. 15,

FIG. 17 is a sectional view of a lens system according to a ninthembodiment of this invention,

FIGS. 18a, 18b, and 18c are views showing abberation curves of the lenssystem shown in FIG. 17,

FIG. 19 is a sectional view of a lens system according to a tenthembodiment of this invention,

FIGS. 20a, 20b, and 20c are views showing aberration curves of the lenssystem shown in FIG. 19,

FIG. 21 is a sectional view of a lens system according to an eleventhembodiment of this invention,

FIGS. 22a, 22b, and 22c are views showing curves of the lens systemshown in FIG. 21,

FIG. 23 is a sectional view of a lens system according to a twelfthembodiment of this invention,

FIGS. 24a, 24b, and 24c are views showing aberration curves of the lenssystem shown in FIG. 23,

FIG. 25 is a sectional view of a lens system according to a thirteenthembodiment of this invention,

FIGS. 26a, 26b, and 26c are views showing aberration curves of the lenssystem shown in FIG. 25,

FIG. 27 is a sectional view of a lens system according to a fourteenthembodiment of this invention,

FIGS. 28a, 28b, and 28c are views showing aberration curves of the lenssystem shown in FIG. 27,

FIG. 29 is a sectional view of a lens system according to a fifteenthembodiment of this invention,

FIGS. 30a, 30b, and 30c are views showing aberration curves of the lenssystem shown in FIG. 29,

FIG. 31 is a sectional view of a lens system according to a sixteenthembodiment of this invention,

FIGS. 32a, 32b, and 32c are views showing aberration curves of the lenssystem shown in FIG. 31,

FIG. 33 is a sectional view of a lens system according to a seventeenthembodiment of this invention,

FIGS. 34a, 34b, and 34c are views showing aberration curves of the lenssystem shown in FIG. 33,

FIG. 35 is a sectional view of a lens system according to a eighteenthembodiment of this invention,

FIGS. 36a, 36b, and 36c are views showing aberration curves of the lenssystem shown in FIG. 35,

FIG. 37 is a sectional view of a lens system according to a nineteenthembodiment of this invention,

FIGS. 38a, 38b, and 38c are views showing aberration curves of the lenssystem shown in FIG. 37,

FIG. 39 is a sectional view of a lens system according to a twentiethembodiment of this invention, and

FIGS. 40a, 40b, and 40c are views showing curves of the lens systemshown in FIG. 39.

DESCRIPTION OF THE PREFERRED EMBODIMENT

FIGS. 1, 3 and 5 are sectional views showing lens systems according to afirst to a third embodiments of this invention, respectively. Each ofthese lens systems comprises a three group, three component lens systemincluding, from the left side opposed to an object, a first, positivemeniscus lens element having a convex surface directed to the object, asecond, biconcave lens element, and a third, biconvex lens element. Eachlens system has an F-number F10 and an angle of view 2 ω=45.2°.

These lens systems satisfy the following conditional expressions:##EQU1## where f is a focal length of each entire system, f₁ is a focallength of the first lens element, f₂ is a focal length of the secondlens element, ν₁ is Abbe number of the first lens element, ν₃ is Abbenumber of the third lens element, d₄ is an axial distance between thesecond and third lens elements, N₁ is a refractive index at line d ofthe first lens element, N₃ is a refractive index at line d of the thirdlens element, r₄ is a radius of curvature of the rear surface of thesecond lens element, and r₅ is a radius of curvature of the frontsurface of the third lens element.

The conditional expression [1] is one for determining the sum of focallengths of the first and second lens elements and for suppressing mainlyspherical aberration. Compensation for spherical aberration will beexcessive in the event of a deviation from the upper limit of theconditional expression [1]. Below its lower limit, compensation forspherical aberration becomes insufficient and astigmatism becomesexcessive, thereby causing a tilt of the image plane.

The conditional expression [2] is one for determining the axial distancebetween the second and third lens elements. Coma flare becomes excessivein the event of a deviation from the lower limit, thereby reducing thecontrast of an image. Above its upper limit, compensation for distortionbecomes insufficient. This produces the undesirable result of enlargingthe lens.

The conditional expression [3] shows a condition regarding Abbe numbersof the first and third lens elements for compensating for chromaticaberration. A sufficient compensation for chromatic aberration isimpossible in the event of a deviation from its upper limit or lowerlimit.

The conditional expression [4] shows a condition regarding therefractive index of a material forming the first and third lens elementsfor compensating for various aberrations. A sufficient compensation forcoma and distortion is impossible in the event of a deviation from thisconditional expression.

The conditional expression [5] shows a condition regarding an air lensbetween the second and third lens elements for reliably compensating forcoma, spherical aberration and the like. In the event of a deviationfrom its upper limit, comas become excessive and compensation forspherical aberration becomes insufficient. Below its lower limited,compensation for spherical aberration becomes excessive.

In addition, image plane characteristics become poor with adeterioration in performance occurring in peripheral regions.

In each of the lens systems according to the first to third embodimentsof this invention, one of the three lens elements is formed of plasticwhich allows the lens system to be lightweight and enables massproduction through a shaping process. By providing the plastic lenselement with an aspheric surface or surfaces, an increased freedom issecured for aberration compensation, to be able to compensate forvarious aberrations even with a reduced total thickness of the lenses.Moreover, each lens system having the improved performance, although itincludes only three lens elements, realizes excellent image formingcharacteristics comparable to or exceeding those of the known lenssystem used for copying purposes.

                                      TABLE 1                                     __________________________________________________________________________    f = 180 FNo. = 10.0                                                           RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT.IND.(Nd)                                                                         ABBE No.(νd)                              __________________________________________________________________________    r.sub.1                                                                            30.69                                                                               d.sub.1                                                                            6.40  N.sub.1                                                                            1.7620                                                                              ν.sub.1                                                                        40.4                                     r.sub.2                                                                            59.19                                                                               d.sub.2                                                                            1.75                                                           r.sub.3 *                                                                         -359.51                                                                             d.sub.3                                                                            1.60  N.sub.2                                                                            1.5840                                                                              ν.sub.2                                                                        31.0                                     r.sub.4                                                                            31.96                                                                               d.sub.4                                                                            6.61                                                          r.sub.5                                                                            154.79                                                                              d.sub.5                                                                            3.71  N.sub.3                                                                            1.6710                                                                              ν.sub.3                                                                        51.7                                     r.sub.6                                                                            -101.99                                                                  Σd = 20.06                                                              __________________________________________________________________________    ASPHERICAL SURFACE COEFFICIENT                                                r.sub.3 :A.sub.2 =                                                                 0.0,     A.sub.3 =                                                                         0.0,     A.sub.4 =                                                                         0.10187 × 10.sup.-6                      A.sub.5 =                                                                          0.0,     A.sub.6 =                                                                         -0.33078 × 10.sup.-8,                                                            A.sub.7 =                                                                         0.0                                            A.sub.8 =                                                                          0.42019 × 10.sup.-10,                                                            A.sub.9 =                                                                         0.0,     A.sub.10 =                                                                        -0.34244 × 10.sup.- 12                   A.sub.11 =                                                                         0.0,     A.sub.12 =                                                                        0.13075 × 10.sup.-14,                                                            A.sub.13 =                                                                        0.0                                            A.sub.14 =                                                                         0.0,     A.sub.15 =                                                                        0.0,     A.sub.16 =                                                                        0.0                                            __________________________________________________________________________

Tables 1 to 3 show numeric values for radii of curvature, axialdistances, refractive indices at line d and Abbe numbers of the lenselements in the respective embodiments. In each of these embodiments,the second lens element has an aspheric surface opposed to the firstlens element, and coefficients of the aspheric surface are shown in thebottom of each table.

                                      TABLE 2                                     __________________________________________________________________________    f = 180 FNo. = 10.0                                                           RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT.IND.(Nd)                                                                         ABBE No.(νd)                              __________________________________________________________________________    r.sub.1                                                                            30.63                                                                               d.sub.1                                                                            6.00  N.sub.1                                                                            1.7620                                                                              ν.sub.1                                                                        40.4                                     r.sub.2                                                                            60.85                                                                               d.sub.2                                                                            1.99                                                           r.sub.3 *                                                                         -314.28                                                                             d.sub.3                                                                            1.59  N.sub.2                                                                            1.5840                                                                              ν.sub.2                                                                        31.0                                     r.sub.4                                                                            31.60                                                                               d.sub.4                                                                            6.48                                                          r.sub.5                                                                            150.13                                                                              d.sub.5                                                                            3.71  N.sub.3                                                                            1.6783                                                                              ν.sub.3                                                                        49.0                                     r.sub.6                                                                            -104.14                                                                  Σd = 19.77                                                              __________________________________________________________________________    ASPHERICAL SURFACE COEFFICIENT                                                r.sub.3 :A.sub.2 =                                                                 0.0,     A.sub.3 =                                                                         0.0,     A.sub.4 =                                                                         0.31706 × 10.sup.-6                      A.sub.5 =                                                                          0.0,     A.sub.6 =                                                                         -0.33081 × 10.sup.-8,                                                            A.sub.7 =                                                                         0.0                                            A.sub.8 =                                                                          0.38113 × 10.sup.-10,                                                            A.sub.9 =                                                                         0.0,     A.sub.10 =                                                                        -0.34801 × 10.sup.- 12                   A.sub.11 =                                                                         0.0,     A.sub.12 =                                                                        0.16932 × 10.sup.-14,                                                            A.sub.13 =                                                                        0.0                                            A.sub.14 =                                                                         0.0,     A.sub.15 =                                                                        0.0,     A.sub.16 =                                                                        0.0                                            __________________________________________________________________________

The aspheric surface is expressed by x=f(y,z) where x is the opticalaxis and rectangular coordinates y and z are located on a plane of apexx=0. If y² +z² =φ², ##EQU2##

In the above equation, the coefficient of the aspheric surface is thevalue of Ai, and Co is an inverse of the radius of curvature. Use ofsuch an aspheric surface realizes an increased freedom of aberrationcompensation to enable a reliable compensation for various aberrations.

FIGS. 2, 4 and 6 show aberration curves in the first to third embodimentat -1x. Each lens system has a focal length f=180 mm and a half angle ofview ω=22.6°.

                                      TABLE 3                                     __________________________________________________________________________    f = 180 FNo. = 10.0                                                           RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT.IND.(Nd)                                                                         ABBE No.(νd)                              __________________________________________________________________________    r.sub.1                                                                            31.02                                                                               d.sub.1                                                                            6.00  N.sub.1                                                                            1.7810                                                                              ν.sub.1                                                                        44.6                                     r.sub.2                                                                            59.43                                                                               d.sub.2                                                                            1.99                                                           r.sub.3 *                                                                         -347.36                                                                             d.sub.3                                                                            1.60  N.sub.2                                                                            1.5840                                                                              ν.sub.2                                                                        31.0                                     r.sub.4                                                                            32.24                                                                               d.sub.4                                                                            6.70                                                          r.sub.5                                                                            158.04                                                                              d.sub.5                                                                            3.70  N.sub.3                                                                            1.6689                                                                              ν.sub.3                                                                        45.0                                     r.sub.6                                                                            -101.74                                                                  Σd = 19.98                                                              __________________________________________________________________________    ASPHERICAL SURFACE COEFFICIENT                                                r.sub.3 :A.sub.2 =                                                                 0.0,     A.sub.3 =                                                                         0.0,     A.sub.4 =                                                                         0.19315 × 10.sup.-6                      A.sub.5 =                                                                          0.0,     A.sub.6 =                                                                         -0.33084 × 10.sup.-8,                                                            A.sub.7 =                                                                         0.0                                            A.sub.8 =                                                                          0.30302 × 10.sup.-10,                                                            A.sub.9 =                                                                         0.0,     A.sub.10 =                                                                        -0.36069 × 10.sup.- 12                   A.sub.11 =                                                                         0.0,     A.sub.12 =                                                                        0.23325 × 10.sup.-14,                                                            A.sub.13 =                                                                        0.0                                            A.sub.14 =                                                                         0.0,     A.sub.15 =                                                                        0.0,     A.sub.16 =                                                                        0.0                                            __________________________________________________________________________

Table 4 shows numeric values for the foregoing conditional expressionsfor the first to third embodiments, and numeric values for the totalthickness Σd indicative of compactness.

A fourth to a seventh embodiments will be described next. No asphericsurface is employed in these embodiments. FIGS. 7, 9 and 11 shows lensarrangements in these embodiments. Each of the illustrated lens systemsincludes, from the left side opposed to an object, a first, positivemeniscus lens element having a convex surface directed to the object, asecond, biconcave lens element, and a third, biconvex lens element. Thesecond, biconcave lens is formed of a plastic material.

                                      TABLE 4                                     __________________________________________________________________________     0.1f < f.sub.1 + f.sub.2 < 0.2f[1]                                                            0.03f < d.sub.4 < 0.05f[2]                                                              ##STR1##                                                                                 ##STR2##                                                                                   ##STR3##                                                                               Σd          __________________________________________________________________________    EM-  0.145f     0.0367f   46.05      1.7165       0.206    0.111f             BODI-                                                                         MENT 1                                                                        EM-  0.141f     0.0360f   44.7       1.7202       0.210    0.110f             BODI-                                                                         MENT 2                                                                        EM-  0.142f     0.0372f   44.8       1.7250       0.204    0.111f             BODI-                                                                         MENT 3                                                                        __________________________________________________________________________

These lens system satisfy the following conditional expressions:##EQU3## where f is a focal length of each entire system, f₁ is a focallength of the first lens element, f₂ is a focal length of the secondlens element, r₄ is a radius of curvature of the rear surface of thesecond lens element, r₅ is a radius of curvature of the front surface ofthe third lens element, ν₁ and ν₃ are Abbe numbers of the first andthird lens elements, respectively, and d₄ is an axial distance betweenthe second and third lens elements.

The conditional expression [6] is one for determining the sum of focallengths of the first and second lens elements and for suppressing mainlyspherical aberration. Compensation for spherical aberration will beexcessive in the event of a deviation from its upper limit. Below itslower limit, compensation for spherical aberration becomes insufficientand astigmatism becomes excessive, thereby causing a tilt of the imageplane.

The conditional expression [7] shows a ratio in the radius of curvaturebetween the second and third lens elements for reliably compensating forcoma, spherical aberration and the like. In the event of a deviationfrom its upper limit, coma becomes excessive, and compensation forspherical aberration becomes insufficient, thereby reducing the contrastof an image. Below its lower limited, compensation for sphericalaberration becomes excessive. In addition, image plane characteristicsbecome poor with a deterioration in performance occurring in peripheralregions of an image.

The conditional expression [8] shows a condition regarding Abbe numbersof the first and third lens elements for compensating for chromaticaberration. A sufficient compensation for chromatic aberration isimpossible in the event of a deviation from its upper limit or lowerlimit.

The conditional expression [9] is one for determining the axial distancebetween the second and third lens elements. In the event of a deviationfrom its upper limit or lower limit, compensation for distortion becomesinsufficient. A deviation from the upper limit produces the undesirableresult of enlarging the lens.

                                      TABLE 5                                     __________________________________________________________________________    f = 180 FNo. = 8.0                                                            RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT.IND.(Nd)                                                                         ABBE No.(νd)                              __________________________________________________________________________    r.sub.1                                                                            36.24                                                                               d.sub.1                                                                            7.20  N.sub.1                                                                            1.7810                                                                              ν.sub.1                                                                        44.6                                     r.sub.2                                                                            95.84                                                                               d.sub.2                                                                            3.30                                                          r.sub.3                                                                            -870.98                                                                             d.sub.3                                                                            2.31  N.sub.2                                                                            1.5840                                                                              ν.sub.2                                                                        31.0                                     r.sub.4                                                                            33.44                                                                               d.sub.4                                                                            11.61                                                         r.sub.5                                                                            167.05                                                                              d.sub.5                                                                            4.00  N.sub.3                                                                            1.6661                                                                              ν.sub.3                                                                        48.0                                     r.sub.6                                                                            -168.83                                                                  Σd = 28.41                                                              __________________________________________________________________________

                                      TABLE 6                                     __________________________________________________________________________    f =  180 FNo. = 10.0                                                          RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT.IND.(Nd)                                                                         ABBE No.(νd)                              __________________________________________________________________________    r.sub.1                                                                            38.07                                                                               d.sub.1                                                                            7.20  N.sub.1                                                                            1.7810                                                                              ν.sub.1                                                                        44.6                                     r.sub.2                                                                            100.56                                                                              d.sub.2                                                                            4.54                                                          r.sub.3                                                                            -619.89                                                                             d.sub.3                                                                            2.30  N.sub.2                                                                            1.5840                                                                              ν.sub.2                                                                        31.0                                     r.sub.4                                                                            35.26                                                                               d.sub.4                                                                            11.75                                                         r.sub.5                                                                            165.86                                                                              d.sub.5                                                                            4.81  N.sub.3                                                                            1.6935                                                                              ν.sub.3                                                                        50.3                                     r.sub.6                                                                            -178.80                                                                  Σd = 30.60                                                              __________________________________________________________________________

                                      TABLE 7                                     __________________________________________________________________________    f =  180 FNo. = 10.0                                                          RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT.IND.(Nd)                                                                         ABBE No.(νd)                              __________________________________________________________________________    r.sub.1                                                                            38.14                                                                               d.sub.1                                                                            8.50  N.sub.1                                                                            1.7885                                                                              ν.sub.1                                                                        45.7                                     r.sub.2                                                                            81.78                                                                               d.sub.2                                                                            3.20                                                          r.sub.3                                                                            -330.87                                                                             d.sub.3                                                                            2.70  N.sub.2                                                                            1.5840                                                                              ν.sub.2                                                                        31.0                                     r.sub.4                                                                            37.55                                                                               d.sub.4                                                                            9.23                                                          r.sub.5                                                                            164.21                                                                              d.sub.5                                                                            4.50  N.sub.3                                                                            1.7003                                                                              ν.sub.3                                                                        47.7                                     r.sub.6                                                                            -133.90                                                                  Σd = 28.13                                                              __________________________________________________________________________

Tables 5 to 8 show numeric values for radii of curvature, axialdistances, refractive indices at line d and Abbe numbers of the fourthto seventh embodiments. FIGS. 8, 10 and 12 show aberration curves in thefourth to seventh embodiments at -1x. Each lens system has a focallength f=180 mm, F-number 8 to 10 and a half angle of view ω=22.6°.Table 9 shows numeric values for the foregoing conditional expressions[6] through [9] for the fourth to seventh embodiments, and numericvalues for the total thickness Σd indicative of compactness.

                                      TABLE 8                                     __________________________________________________________________________    f = 180 FNo. = 10.0                                                           RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT.IND.(Nd)                                                                         ABBE No.(νd)                              __________________________________________________________________________    r.sub.1                                                                            31.53                                                                               d.sub.1                                                                            7.20  N.sub.1                                                                            1.7200                                                                              ν.sub.1                                                                        42.0                                     r.sub.2                                                                            150.02                                                                              d.sub.2                                                                            1.58                                                          r.sub.3                                                                            -799.62                                                                             d.sub.3                                                                            2.30  N.sub.2                                                                            1.5840                                                                              ν.sub.2                                                                        31.0                                     r.sub.4                                                                            27.85                                                                               d.sub.4                                                                            14.21                                                         r.sub.5                                                                            173.54                                                                              d.sub.5                                                                            4.00  N.sub.3                                                                            1.6201                                                                              ν.sub.3                                                                        49.8                                     r.sub.6                                                                            -211.04                                                                  Σd = 29.29                                                              __________________________________________________________________________

An eighth to an eleventh embodiments will be described next. FIGS. 15,17, 19 and 21 are sectional views showing lens systems in theseembodiments. Each of the lens systems comprises a three group, threecomponent lens system including, from the left side opposed to anobject, a first, positive meniscus lens element having a convex surfacedirected to the object, a second, biconcave lens element, and a third,biconvex lens element. Each lens system has an F-number F10 and an angleof view 2ω=45.2°.

These lens systems satisfy the following conditional expressions:

    0.015f<d.sub.2 <0.025f                                     [10]

    0.05f<d.sub.4 <0.15f                                       [11]

    0.04f<f.sub.1 +f.sub.2 <0.06f                              [12]

    1.65<N.sub.1                                               [ 13]

    35<ν.sub.1 <50                                          [14]

where f is a focal length of each entire system, d₂ is an axial distancebetween the first and second lens elements, d₄ is an axial distancebetween the second and third lens elements, f₁ is a focal length of thefirst lens elements, F₂ is a focal length of the second lens element, N₁is a refractive index at line d of the first lens element, and ν₁ isAbbe number of the first lens element.

                                      TABLE 9                                     __________________________________________________________________________               0.04f < f.sub.1 + f.sub.2 < 0.2f[6]                                                      ##STR4##                                                                               ##STR5##   0.05f < d.sub.4                                                                         Σd]                 __________________________________________________________________________    EMBODIMENT 4                                                                            0.087f     0.200    46.3       0.0645f   0.158f                     EMBODIMENT 5                                                                            0.098f     0.213    47.5       0.0652f   0.170f                     EMBODIMENT 6                                                                            0.144f     0.229    46.7       0.0513f   0.156f                     EMBODIMENT 7                                                                            0.045f     0.160    45.9       0.079f    0.163f                     __________________________________________________________________________

The conditional expression [10] is one for determining the axialdistance between the first and second lens elements. In the event of adeviation from this condition, it is difficult to compensate fordistortion, magnification and chromatic aberration in a balanced manner.

The conditional expression [11] is one for determining the axialdistance between the second and third lens elements. Coma flare becomesexcessive in the event of a deviation from the lower limit, therebyreducing the contrast of an image. Above its upper limit, compensationfor distortion becomes insufficient. This produces the undesirableresult of enlarging the lens.

The conditional expression [12] is one for determining the sum of focallengths of the first and second lens elements and for suppressing mainlyspherical aberration. Compensation for spherical aberration will beexcessive in the event of a deviation from the upper limit of theconditional expression [12]. Below its lower limit, compensation forspherical aberration becomes insufficient and astigmatism becomesexcessive, thereby causing a tilt of the image plane.

The conditional expressions [13] and [14] both show conditions fordetermining a material for the first lens element. A deviation from theexpression [13] results in an increase in astigmatic difference, and aninsufficient compensation for coma. A deviation from the expression [14]results in an insufficient compensation for chromatic aberration.

In each of the lens systems according to the eighth to eleventhembodiments, two of the three lens elements are formed of plastic.Specifically, the second lens element is formed of polycarbonate, andthe third lens element of acrylic resin. This construction allows thelens system to be lightweight and enables mass production through ashaping process. Although asymmetric, these lens systems reliablycompensate for various aberrations including distortion.

                                      TABLE 10                                    __________________________________________________________________________    f = 180 FNo. = 10.0                                                           RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT.IND.(Nd)                                                                         ABBE No.(νd)                              __________________________________________________________________________    r.sub.1                                                                            36.68                                                                               d.sub.1                                                                            7.70  N.sub.1                                                                            1.7859                                                                              ν.sub.1                                                                        43.9                                     r.sub.2                                                                            168.75                                                                              d.sub.2                                                                            3.80                                                          r.sub.3                                                                            -629.34                                                                             d.sub.3                                                                            2.00  N.sub.2                                                                            1.5840                                                                              ν.sub.2                                                                        31.0                                     r.sub.4                                                                            30.36                                                                               d.sub.4                                                                            18.16                                                         r.sub.5                                                                            194.91                                                                              d.sub.5                                                                            5.00  N.sub.3                                                                            1.4914                                                                              ν.sub.3                                                                        57.8                                     r.sub.6                                                                            -136.29                                                                  Σd = 36.66                                                              __________________________________________________________________________

Tables 10 to 13 show numeric values for radii of curvature, axialdistances, refractive indices at line d and Abbe numbers of the eighthto eleventh embodiments. FIGS. 16, 18, 20 and 22 show aberration curvesin the eighth to eleventh embodiments at -1x. Each lens system has afocal length f=180 mm, F-number 10 and a half angle of view ω=22.6°.

                                      TABLE 11                                    __________________________________________________________________________    f = 180 FNo. = 10.0                                                           RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT.IND.(Nd)                                                                         ABBE No.(νd)                              __________________________________________________________________________    r.sub.1                                                                            34.48                                                                               d.sub.1                                                                            8.00  N.sub.1                                                                            1.7200                                                                              ν.sub.1                                                                        42.0                                     r.sub.2                                                                            237.28                                                                              d.sub.2                                                                            4.00                                                          r.sub.3                                                                            -309.32                                                                             d.sub.3                                                                            2.00  N.sub.2                                                                            1.5840                                                                              ν.sub.2                                                                        31.0                                     r.sub.4                                                                            28.96                                                                               d.sub.4                                                                            17.08                                                         r.sub.5                                                                            174.74                                                                              d.sub.5                                                                            5.50  N.sub.3                                                                            1.4914                                                                              ν.sub.3                                                                        57.8                                     r.sub.6                                                                            -129.06                                                                  Σd = 36.58                                                              __________________________________________________________________________

Table 14 shows numeric values for the foregoing conditional expressionsfor the eighth to eleventh embodiments, and numeric values for the totalthickness Σd indicative of compactness.

A twelfth to a sixteenth embodiments will be described next. Theseembodiments include a second and a third lens elements formed of plasticand each defining at least one aspheric surface.

                                      TABLE 12                                    __________________________________________________________________________    f = 180 FNo. = 10.0                                                           RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT.IND.(Nd)                                                                         ABBE No.(νd)                              __________________________________________________________________________    r.sub.1                                                                            37.28                                                                               d.sub.1                                                                            7.70  N.sub.1                                                                            1.7856                                                                              ν.sub.1                                                                        42.8                                     r.sub.2                                                                            173.81                                                                              d.sub.2                                                                            4.00                                                          r.sub.3                                                                            -586.23                                                                             d.sub.3                                                                            2.40  N.sub.2                                                                            1.5840                                                                              ν.sub.2                                                                        31.0                                     r.sub.4                                                                            30.73                                                                               d.sub.4                                                                            18.11                                                         r.sub.5                                                                            188.68                                                                              d.sub.5                                                                            5.30  N.sub.3                                                                            1.4914                                                                              ν.sub.3                                                                        57.8                                     r.sub.6                                                                            -137.51                                                                  Σd = 37.51                                                              __________________________________________________________________________

                                      TABLE 13                                    __________________________________________________________________________    f =  180 FNo. = 10.0                                                          RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT.IND.(Nd)                                                                         ABBE No.(νd)                              __________________________________________________________________________    r.sub.1                                                                            38.19                                                                               d.sub.1                                                                            7.70  N.sub.1                                                                            1.8205                                                                              ν.sub.1                                                                        43.0                                     r.sub.2                                                                            152.57                                                                              d.sub.2                                                                            3.80                                                          r.sub.3                                                                            -909.80                                                                             d.sub.3                                                                            2.00  N.sub.2                                                                            1.5840                                                                              ν.sub.2                                                                        31.0                                     r.sub.4                                                                            31.56                                                                               d.sub.4                                                                            18.44                                                         r.sub.5                                                                            198.10                                                                              d.sub.5                                                                            5.00  N.sub.3                                                                            1.4914                                                                              ν.sub.3                                                                        47.8                                     r.sub.6                                                                            -142.54                                                                  Σd = 36.94                                                              __________________________________________________________________________

FIGS. 23, 25, 27, 29 and 31 are sectional views showing lens systems inthese embodiments. Each of the lens systems includes, from the leftside, a first, positive meniscus lens element having a convex surfacedirected outwardly of the system, a second, concave lens element, and athird, convex lens element. The second and third lens elements areformed of plastic. Specifically, the second lens element is formed ofpolycarbonate, and the third lens element of acrylic resin. Thisconstruction allows the lens system to be lightweight and enables massproduction through a shaping process.

These lens systems satisfy the following conditional expressions:

    0.005f<d.sub.2 0.015f                                      [15]

    0.05f<d.sub.4 <0.15f                                       [16]

    0.015f<f.sub.1 +f.sub.2 <0.05f                             [17]

    1.65<N.sub.1                                               [ 18]

    35<ν.sub.1 <50                                          [19]

where f is a focal length of each entire system, d₂ is an axial distancebetween the first and second lens elements, d₄ is an axial distancebetween the second and third lens elements, f₁ is a focal length of thefirst lens element, f₂ is a focal length of the second lens element, N₁is a refractive index at line d of the first lens element, and ν₁ isAbbe number of the first lens element.

                  TABLE 14                                                        ______________________________________                                                 [10]          [11]                                                            0.015f < d.sub.2 < 0.025f                                                                   0.05f < d.sub.4 < 0.15f                                ______________________________________                                        EMBODIMENT 0.0211f         0.1009f                                            EMBODIMENT 0.0222f         0.0949f                                            9                                                                             EMBODIMENT 0.0222f         0.1006f                                            10                                                                            EMBODIMENT 0.0211f         0.1024f                                            11                                                                            ______________________________________                                                 [12]          [13]                                                            0.04f < f.sub.1 + f.sub.2 < 0.06f                                                           1.65 < N.sub.1                                         ______________________________________                                        EMBODIMENT 0.0478f         1.7859                                             EMBODIMENT 0.0548f         1.7200                                             9                                                                             EMBODIMENT 0.0501f         1.7856                                             10                                                                            EMBODIMENT 0.0449f         1.8025                                             11                                                                            ______________________________________                                                 [14]                                                                          35 < ν.sub.1 < 50                                                                        Σd                                               ______________________________________                                        EMBODIMENT 43.9            0.204f                                             EMBODIMENT 42.0            0.203f                                             9                                                                             EMBODIMENT 42.8            0.208f                                             10                                                                            EMBODIMENT 43.0            0.205f                                             11                                                                            ______________________________________                                    

The conditional expression [15] is one for determining the axialdistance between the first and second lens elements. In the event of adeviation from this condition, it is difficult to compensate fordistortion, magnification and chromatic aberration in a balanced manner.

The conditional expression [16] is one for determining the axialdistance between the second and third lens elements. Coma flare becomesexcessive in the event of a deviation from the lower limit, therebyreducing the contrast of an image. Above its upper limit, compensationfor distortion becomes insufficient. This produces the undesirableresult of enlarging the lens.

The conditional expression [17] is one for determining the sum of focallens of the first and second lens elements and for suppressing mainlyspherical aberration. Compensation for spherical aberration will beexcessive in the event of a deviation from the upper limit of theconditional expression [17]. Below its lower limit, compensation forspherical aberration becomes insufficient and astigmatism becomesexcessive, thereby causing a tilt of the image plane.

The conditional expressions [18] and [19] both show conditions fordetermining a material for the first lens element. A deviation from theexpression [18] results in an increase in astigmatic difference, and aninsufficient compensation for coma. A deviation from the expression [19]results in an insufficient compensation for chromatic aberration.

Tables 15 to 19 show numeric values for radii of curvature, axialdistances, refractive indices at line d and Abbe numbers of the twelfthto sixteenth embodiments. FIGS. 24, 26, 28, 30 and 32 show aberrationcurves in the twelfth to sixteenth embodiments at -1x. Each lens systemhas a focal length f=180 mm, F-number 10 and a half angle of viewω=22.6°. Table 20 shows numeric values for the foregoing conditionalexpressions [15] through [19] for the twelfth to sixteenth embodiments,and numeric values for the total thickness Σd indicative of compactness.

The twelfth to sixteenth embodiments have the second and third lenselements defining aspheric surfaces. In the twelfth to fourteenthembodiments, the second lens element defines an aspheric surface opposedto the third lens element. In the fifteenth embodiment, the second lenselement defines an aspheric surface opposed to the first lens element.In the sixteen embodiment, the second lens element defines an asphericsurface opposed to the third lens element, and the third lens elementdefines an aspheric surface directed outwardly of the lens system.Coefficients of the aspheric surfaces are shown in the bottoms of Tables15 to 19.

                                      TABLE 15                                    __________________________________________________________________________    f = 180    FNo. = 10.0                                                        __________________________________________________________________________    RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT. IND (Nd)                                                                         ABBE No. (νd)                            __________________________________________________________________________    r.sub.1                                                                          34.28                                                                                 d.sub.1 7.70                                                                             N.sub.1 1.7856                                                                            ν.sub.1 42.8                             r.sub.2                                                                          158.64                                                                                d.sub.2 2.00                                                       r.sub.3                                                                          -1574.11                                                                              d.sub.3 2.40                                                                             N.sub.2 1.5840                                                                            ν.sub.2 31.0                              r.sub.4 *                                                                       28.51                                                                                  d.sub.4 18.37                                                     r.sub.5                                                                          189.75                                                                                d.sub.5 5.30                                                                             N.sub.3 1.4914                                                                            ν.sub.3 57.8                             r.sub.6                                                                          -162.41                                                                               Σd = 35.77                                                   __________________________________________________________________________    ASPHERICAL SURFACE COEFFECIENT                                                __________________________________________________________________________    r.sub.4 :                                                                       A.sub.2 = 0.0,                                                                             A.sub.3 = 0.0,                                                                             A.sub.4 = 0.24564 × 10.sup.-7                 A.sub.5 = 0.0,                                                                             A.sub.6 = 0.20753 × 10.sup.-9,                                                       A.sub.7 = 0.0                                       A.sub.8 = 0.17162 × 10.sup.-15 ,                                                     A.sub.9 = 0.0,                                                                             A.sub.10 = -0.16968 × 10.sup.-16              A.sub.11 = 0.0,                                                                            A.sub.12 = -0.34161 × 10.sup.-18,                                                    A.sub.13 = 0.0                                      A.sub.14 = -0.13799 × 10.sup.-17,                                                    A.sub.15 = 0.0,                                                                            A.sub.16 = 0.0                                    __________________________________________________________________________

                                      TABLE 16                                    __________________________________________________________________________    f = 180    FNo. = 10.0                                                        __________________________________________________________________________    RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT. IND (Nd)                                                                         ABBE No. (νd)                            __________________________________________________________________________    r.sub.1                                                                          35.27                                                                                 d.sub.1 7.70                                                                             N.sub.1 1.7995                                                                            ν.sub.1 42.3                             r.sub.2                                                                          155.01                                                                                d.sub.2 1.50                                                       r.sub.3                                                                          -7768.19                                                                              d.sub.3 3.70                                                                             N.sub.2 1.5840                                                                            ν.sub.2 31.0                              r.sub.4 *                                                                       29.05                                                                                  d.sub.4 18.36                                                     r.sub.5                                                                          182.24                                                                                d.sub.5 5.30                                                                             N.sub.3 1.4914                                                                            ν.sub.3 57.8                             r.sub.6                                                                          -179.80                                                                               Σd = 36.56                                                   __________________________________________________________________________    ASPHERICAL SURFACE COEFFECIENT                                                __________________________________________________________________________    r.sub.4 :                                                                       A.sub.2 = 0.0,                                                                             A.sub.3 = 0.0,                                                                             A.sub.4 = 0.59240 × 10.sup.-7                 A.sub.5 = 0.0,                                                                             A.sub.6 = 0.51484 × 10.sup.-9,                                                       A.sub.7 = 0.0                                       A.sub.8 = 0.75687 × 10.sup.-15 ,                                                     A.sub.9 = 0.0,                                                                             A.sub.10 = -0.10666 × 10.sup.-15              A.sub.11 = 0.0,                                                                            A.sub.12 = -0.31771 × 10.sup.-18,                                                    A.sub.13 = 0.0                                      A.sub.14 = -0.13002 × 10.sup.-17,                                                    A.sub.15 = 0.0,                                                                            A.sub.16 = 0.0                                    __________________________________________________________________________

The description made of the aspheric surface in the first to thirdembodiments applies to the twelfth to sixteenth embodiments also.

A seventeenth to a twentieth embodiments will be described next. Theseembodiments also include a second and a third lens elements formed ofplastic and defining aspheric surfaces.

FIGS. 33, 35, 37 and 39 are sectional views showing lens systems inthese embodiments. Each of the lens systems includes, from the left sideopposed to an object, a first, positive meniscus lens element having aconvex surface directed toward the object, a second, concave lenselement, and a third, convex lens element. The second and third lenselements are formed of plastic. Specifically, the second lens element isformed of polycarbonate, and the third lens element of acrylic resin.This construction allows the lens system to be lightweight and enablesmass production through a shaping process.

                                      TABLE 17                                    __________________________________________________________________________    f = 180    FNo. = 10.0                                                        __________________________________________________________________________    RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT. IND (Nd)                                                                         ABBE No. (νd)                            __________________________________________________________________________    r.sub.1                                                                           30.21                                                                                d.sub.1 5.00                                                                             N.sub.1 1.7620                                                                            ν.sub.1 40.4                             r.sub.2                                                                           110.81                                                                               d.sub.2 1.80                                                       r.sub.3                                                                           926.84                                                                               d.sub.3 3.70                                                                             N.sub.2 1.5840                                                                            ν.sub.2 31.0                              r.sub.4 *                                                                        25.95                                                                                 d.sub.4 13.37                                                     r.sub.5                                                                           110.96                                                                               d.sub.5 5.30                                                                             N.sub.3 1.4914                                                                            ν.sub.3 57.8                             r.sub.6                                                                           -269.12                                                                              Σd = 19.17                                                   __________________________________________________________________________    ASPHERICAL SURFACE COEFFICIENT                                                __________________________________________________________________________    r.sub.4 :                                                                       A.sub.2 = 0.0,                                                                             A.sub.3 = 0.0,                                                                             A.sub.4 = 0.90539 × 10.sup.-7                 A.sub.5 = 0.0,                                                                             A.sub.6 = 0.89903 × 10.sup.-9,                                                       A.sub.7 = 0.0                                       A.sub.8 = 0.12844 × 10.sup.-14,                                                      A.sub.9 = 0.0,                                                                             A.sub.10 = -0.11284 × 10.sup.-15              A.sub.11 = 0.0,                                                                            A.sub.12 = -0.33922 × 10.sup.-18,                                                    A.sub.13 = 0.0                                      A.sub.14 = -0.10720 × 10.sup.-16,                                                    A.sub.15 = 0.0,                                                                            A.sub.16 = 0.0                                    __________________________________________________________________________

These lens systems satisfy the following conditional expressions:

    0.05f<d.sub.2 <0.025f                                      [20]

    0.05f<d.sub.4 <0.08f                                       [21]

    1.75<N.sub.1 <1.85                                         [22]

    35<ν.sub.1 <50                                          [23] ##EQU4## where f is a focal length of each entire system, d.sub.2 is an axial distance between the first and second lens elements, d.sub.4 is an axial distance between the second and third lens elements, f.sub.1 is a focal length of the first lens element, f.sub.2 is a focal length of the second lens element, N.sub.1 is a refractive index at line d of the first lens element, ν.sub.1 is Abbe number of the first lens element, r.sub.4 is a radius of curvature of the surface of the second lens element opposed to the third lens element, and r.sub.5 is a radius of curvature of the surface of the third lens element opposed to the second lens element.

                                      TABLE 18                                    __________________________________________________________________________    f = 180    FNo. = 10.0                                                        __________________________________________________________________________    RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT. IND (Nd)                                                                         ABBE No. (νd)                            __________________________________________________________________________    r.sub.1                                                                           34.64                                                                                d.sub.1 7.70                                                                             N.sub.1 1.7995                                                                            ν.sub.1 42.3                             r.sub.2                                                                           137.06                                                                               d.sub.2 1.50                                                        r.sub.3*                                                                         1639.40                                                                              d.sub.3 3.70                                                                             N.sub.2 1.5840                                                                            ν.sub.2 31.0                              r.sub.4 *                                                                        28.56                                                                                 d.sub.4 17.74                                                     r.sub.5                                                                           159.98                                                                               d.sub.5 5.30                                                                             N.sub.3 1.4914                                                                            ν.sub.3 57.8                             r.sub.6                                                                           -202.29                                                                              Σd = 34.89                                                   __________________________________________________________________________    ASPHERICAL SURFACE COEFFICIENT                                                __________________________________________________________________________    r.sub.3 :                                                                       A.sub.2 = 0.0,                                                                             A.sub.3 = 0.0,                                                                             A.sub.4 = -0.15797 × 10.sup.-6                A.sub.5 = 0.0,                                                                             A.sub.6 = 0.20725 × 10.sup.-8,                                                       A.sub.7 = 0.0                                       A.sub.8 = -0.35825 × 10.sup. -10,                                                    A.sub.9 = 0.0,                                                                             A.sub.10 = 0.15895 × 10.sup.-12               A.sub.11 = 0.0,                                                                            A.sub.12 = 0.24109 × 10.sup.-15,                                                     A.sub.13 = 0.0                                      A.sub.14 = -0.13211 × 10.sup.-17,                                                    A.sub.15 = 0.0,                                                                            A.sub.16 = 0.0                                    r.sub.4:                                                                        A.sub.2 = 0.0,                                                                             A.sub.3 = 0.0,                                                                             A.sub.4 = 0.14540 × 10.sup.-8                 A.sub.5 = 0.0,                                                                             A.sub.6 = 0.22058 × 10.sup.-10,                                                      A.sub.7 = 0.0                                       A.sub.8 = 0.70808 × 10.sup.-15,                                                      A.sub.9 = 0.0,                                                                             A.sub.10 = -0.14977 × 10.sup.-16              A.sub.11 = 0.0,                                                                            A.sub.12 = -0.31317 × 10.sup.-18,                                                    A.sub.13 = 0.0                                      A.sub.14 = 0.77389 × 10.sup.-17,                                                     A.sub.15 = 0.0,                                                                            A.sub.16 = 0.0                                    __________________________________________________________________________

                                      TABLE 19                                    __________________________________________________________________________    f = 180    FNo. = 10.0                                                        __________________________________________________________________________    RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT. IND (Nd)                                                                         ABBE No. (νd)                            __________________________________________________________________________    r.sub.1                                                                           30.80                                                                                d.sub.1 6.30                                                                             N.sub.1 1.7856                                                                            ν.sub.1 42.8                             r.sub.2                                                                           100.71                                                                               d.sub.2 2.00                                                       r.sub.3                                                                           314.41                                                                               d.sub.3 2.50                                                                             N.sub.2 1.5840                                                                            ν.sub.2 31.0                              r.sub.4 *                                                                        26.62                                                                                 d.sub.4 19.38                                                     r.sub.5                                                                           91.39                                                                                d.sub.5 4.81                                                                             N.sub.3 1.4914                                                                            ν.sub.3 57.8                              r.sub.6*                                                                         1041.84                                                                              Σd = 34.89                                                   __________________________________________________________________________    ASPHERICAL SURFACE COEFFICIENT                                                __________________________________________________________________________    r.sub.4 :                                                                       A.sub.2 = 0.0,                                                                             A.sub.3 = 0.0,                                                                             A.sub.4 = 0.47833 × 10.sup.-7                 A.sub.5 = 0.0,                                                                             A.sub.6 = 0.42846 × 10.sup.-8,                                                       A.sub.7 = 0.0                                       A.sub.8 = 0.10513 × 10.sup.-15,                                                      A.sub.9 = 0.0,                                                                             A.sub.10 = 0.53716 × 10.sup.-17               A.sub.11 = 0.0,                                                                            A.sub.12 = -0.24619 × 10.sup.-14,                                                    A.sub.13 = 0.0                                      A.sub.14 = 0.12123 × 10.sup.-16,                                                     A.sub.15 = 0.0,                                                                            A.sub.16 = -0.11447 × 10.sup.19             r.sub.6:                                                                        A.sub.2 = 0.0,                                                                             A.sub.3 = 0.0,                                                                             A.sub.4 = 0.62893 × 10.sup.-6                 A.sub.5 = 0.0,                                                                             A.sub.6 = 0.80976 × 10.sup.-8,                                                       A.sub.7 = 0.0                                       A.sub.8 = -0.83956 × 10.sup.-10,                                                     A.sub.9 = 0.0,                                                                             A.sub.10 = 0.19293 × 10.sup.-12               A.sub.11 = 0.0,                                                                            A.sub.12 = 0.13714 × 10.sup.-18,                                                     A.sub.13 = 0.0                                      A.sub.14 = 0.24500 × 10.sup.-17,                                                     A.sub.15 = 0.0,                                                                            A.sub.16 = 0.0                                    __________________________________________________________________________

                  TABLE 20                                                        ______________________________________                                                   [15]            [16]                                                          0.005f < d.sub.2 < 0.015f                                                                     0.05f < d.sub.4 < 0.15f                            ______________________________________                                        EMBODIMENT 0.0111f         0.1021f                                            12                                                                            EMBODIMENT 0.0083f         0.1020f                                            13                                                                            EMBODIMENT 0.0100f         0.0743f                                            14                                                                            EMBODIMENT 0.0083f         0.0986f                                            15                                                                            EMBODIMENT 0.0111f         0.1077f                                            16                                                                            ______________________________________                                                   [17]            [18]                                                          0.015f < f.sub.1 + f.sub.2 < 0.05f                                                            1.65f < N.sub.1                                    ______________________________________                                        EMBODIMENT 0.0348f         1.7856                                             12                                                                            EMBODIMENT 0.0332f         1.7995                                             13                                                                            EMBODIMENT 0.0405f         1.7620                                             14                                                                            EMBODIMENT 0.0350f         1.7995                                             15                                                                            EMBODIMENT 0.0243f         1.7856                                             16                                                                            ______________________________________                                                   [19]                                                                          35 < ν.sub.1 < 50                                                                          Σd                                           ______________________________________                                        EMBODIMENT 42.8            0.199f                                             12                                                                            EMBODIMENT 42.3            0.203f                                             13                                                                            EMBODIMENT 40.4            0.162f                                             14                                                                            EMBODIMENT 42.3            0.200f                                             15                                                                            EMBODIMENT 42.8            0.194f                                             16                                                                            ______________________________________                                    

The conditional expression [20] is one for determining the axialdistance between the first and second lens elements. In the event of adeviation from this condition, it is difficult to compensate fordistortion, magnification and chromatic aberration in a balanced manner.

The conditional expression [21] is one for determining the axialdistance between the second and third lens elements. Coma flare becomesexcessive in the event of a deviation from the lower limit, therebyreducing the contrast of an image. Above its upper limit, compensationfor distortion becomes insufficient. This produces the undesirableresult of enlarging the lens.

The conditional expressions [22] and [23] both show conditions fordetermining a material for the first lens element. A deviation from theexpression [22] results in an increase in astigmatic difference, and aninsufficient compensation for coma. A deviation from the expression [23]results in an insufficient compensation for chromatic aberration.

The conditional expression [24] shows a ratio in radius of curvaturebetween the second and third lens elements for compensating for coma andspherical aberration. In the event of a deviation from its upper limit,coma becomes excessive, and compensation for spherical aberrationbecomes insufficient, thereby reducing contrast of the image. Below itslower limited, compensation for spherical aberration becomes excessive.

In addition, image plane characteristics become poor with adeterioration in performance occurring in peripheral regions.

Further, the seventeenth to twentieth embodiments satisfy the followingconditional expression:

    0.03f<f.sub.1 +f.sub.2 <0.1f

where f₁ is a focal length of the first lens element, and f₂ is a focallength of the second lens element.

This expression is one for determining the sum of focal lengths of thefirst and second lens elements and for suppressing mainly sphericalaberration. Compensation for spherical aberration will be excessive inthe event of a deviation from its upper limit. Below its lower limit,compensation for spherical aberration becomes insufficient andastigmatism becomes excessive, thereby causing a tilt of the imageplane.

Tables 21 to 24 show numeric values for radii of curvature, axialdistances, refractive indices at line d and Abbe numbers of theseventeenth to twentieth embodiments. FIGS. 34, 36, 38 and 40 showaberration curves in the seventeenth to twentieth embodiments at -1x.

Each lens system has a focal length f=180 mm, F-number 10 and a halfangle of view ω=22.6°. Table 25 shows numeric values for the foregoingconditional expressions [20] through [24] for the seventeenth totwentieth embodiments, and numeric values for the total thickness Σdindicative of compactness.

                                      TABLE 21                                    __________________________________________________________________________    f = 180    FNo. = 10.0                                                        __________________________________________________________________________    RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT. IND (Nd)                                                                         ABBE No. (νd)                            __________________________________________________________________________    r.sub.1                                                                           30.52                                                                                d.sub.1 6.30                                                                             N.sub.1 1.7620                                                                            ν.sub.1 40.4                             r.sub.2                                                                           101.79                                                                               d.sub.2 2.00                                                       r.sub.3                                                                           401.88                                                                               d.sub.3 2.50                                                                             N.sub.2 1.5840                                                                            ν.sub.2 31.0                              r.sub.4 *                                                                        24.85                                                                                 d.sub.4 12.13                                                     r.sub.5                                                                           3839.51                                                                              d.sub.5 4.81                                                                             N.sub.3 1.4914                                                                            ν.sub.3 57.8                              r.sub.6*                                                                         -71.24                                                                               Σd = 27.74                                                   __________________________________________________________________________    ASPHERICAL SURFACE COEFFICIENT                                                __________________________________________________________________________    r.sub.4 :                                                                       A.sub.2 = 0.0,                                                                             A.sub.3 = 0.0,                                                                             A.sub.4 = 0.23755 × 10.sup.-5                 A.sub.5 = 0.0,                                                                             A.sub.6 = 0.45129 × 10.sup.-8,                                                       A.sub.7 = 0.0                                       A.sub.8 = 0.10520 × 10.sup.-15 ,                                                     A.sub.9 = 0.0,                                                                             A.sub.10 = 0.53787 × 10.sup.-17               A.sub.11 = 0.0,                                                                            A.sub.12 = -0.42574 × 10.sup.-14,                                                    A.sub.13 = 0.0                                      A.sub.14 = 0.82913 × 10.sup.-16,                                                     A.sub.15 = 0.0,                                                                            A.sub.16 = 0.40424 × 10.sup.-18             r.sub.6:                                                                        A.sub.2 = 0.0,                                                                             A.sub.3 = 0.0,                                                                             A.sub.4 = -0.46571 × 10.sup.-5                A.sub.5 = 0.0,                                                                             A.sub.6 = 0.79477 × 10.sup.-7,                                                       A.sub.7 = 0.0                                       A.sub.8 = -0.12881 × 10.sup.-8,                                                      A.sub.9 = 0.0,                                                                             A.sub.10 = 0.74208 × 10.sup.-11               A.sub.11 = 0.0,                                                                            A.sub.12 = 0.13712 × 10.sup.-18,                                                     A.sub.13 = 0.0                                      A.sub.14 = -0.93002 × 10.sup.-16,                                                    A.sub.15 = 0.0,                                                                            A.sub.16 =  0.0                                   __________________________________________________________________________

In the seventeenth to twentieth embodiments, the second lens elementdefines an aspheric surface r₄ opposed to the third lens element, andthe third lens element defines an aspheric surface r₆ directed outwardlyof the lens system. Coefficients of the aspheric surfaces are shown inthe bottoms of Tables 21 to 24. The description of the aspheric surfaceshas already been made and will not be repeated.

                                      TABLE 22                                    __________________________________________________________________________    f = 180    FNo. = 10.0                                                        __________________________________________________________________________    RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT. IND (Nd)                                                                         ABBE No. (νd)                            __________________________________________________________________________    r.sub.1                                                                           31.43                                                                                d.sub.1 6.30                                                                             N.sub.1 1.7620                                                                            ν.sub.1 40.4                             r.sub.2                                                                           112.27                                                                               d.sub.2 2.00                                                       r.sub.3                                                                           425.45                                                                               d.sub.3 3.00                                                                             N.sub.2 1.5840                                                                            ν.sub.2 31.0                              r.sub.4 *                                                                        24.85                                                                                 d.sub.4 12.13                                                     r.sub.5                                                                           -479.33                                                                              d.sub.5 4.81                                                                             N.sub.3 1.4914                                                                            ν.sub.3 57.8                              r.sub.6*                                                                         -60.30                                                                               Σd = 28.24                                                   __________________________________________________________________________    ASPHERICAL SURFACE COEFFICIENT                                                __________________________________________________________________________    r.sub.4 :                                                                       A.sub.2 = 0.0,                                                                             A.sub.3 = 0.0,                                                                             A.sub.4 = 0.29439 × 10.sup.-5                 A.sub.5 = 0.0,                                                                             A.sub.6 = 0.46134 × 10.sup.-8,                                                       A.sub.7 = 0.0                                       A.sub.8 = 0.10524 × 10.sup.- 15,                                                     A.sub.9 = 0.0,                                                                             A.sub.10 = 0.52927 × 10.sup.-17               A.sub.11 = 0.0,                                                                            A.sub.12 = 0.19481 × 10.sup.-13,                                                     A.sub.13 = 0.0                                      A.sub.14 = -0.27094 × 10.sup.-15,                                                    A.sub.15 = 0.0,                                                                            A.sub.16 = 0.10486 × 10.sup.-17             r.sub.6:                                                                        A.sub.2 = 0.0,                                                                             A.sub.3 = 0.0,                                                                             A.sub.4 = -0.49450 × 10.sup.-5                A.sub.5 = 0.0,                                                                             A.sub.6 = 0.65343 × 10.sup.-7,                                                       A.sub.7 = 0.0                                       A.sub.8 = -0.10859 × 10.sup.-8,                                                      A.sub.9 = 0.0,                                                                             A.sub.10 = 0.61344 × 10.sup.-11               A.sub.11 = 0.0,                                                                            A.sub.12 = 0.13710 × 10.sup.-18,                                                     A.sub.13 = 0.0                                      A.sub.14 = -0.73164 × 10.sup.-16,                                                    A.sub.15 = 0.0,                                                                            A.sub.16  = 0.0                                   __________________________________________________________________________

                                      TABLE 23                                    __________________________________________________________________________    f = 180    FNo. = 10.0                                                        __________________________________________________________________________    RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT. IND (Nd)                                                                         ABBE No. (νd)                            __________________________________________________________________________    r.sub.1                                                                           37.56                                                                                d.sub.1 7.70                                                                             N.sub.1 1.8050                                                                            ν.sub.1 41.0                             r.sub.2                                                                           127.84                                                                               d.sub.2 3.95                                                       r.sub.3                                                                           -545.95                                                                              d.sub.3 2.40                                                                             N.sub.2 1.5840                                                                            ν.sub.2 31.0                              r.sub.4 *                                                                        30.72                                                                                 d.sub.4 13.27                                                     r.sub.5                                                                           216.19                                                                               d.sub.5 5.01                                                                             N.sub.3 1.4914                                                                            ν.sub.3 57.8                              r.sub.6*                                                                         -90.58                                                                               Σd = 32.33                                                   __________________________________________________________________________    ASPHERICAL SURFACE COEFFICIENT                                                __________________________________________________________________________    r.sub.4 :                                                                       A.sub.2 = 0.0,                                                                             A.sub.3 = 0.0,                                                                             A.sub.4 = 0.31405 × 10.sup.-8                 A.sub.5 = 0.0,                                                                             A.sub.6 = 0.13301 × 10.sup.-11,                                                      A.sub.7 = 0.0                                       A.sub.8 = 0.30421 × 10.sup.- 13,                                                     A.sub.9 = 0.0,                                                                             A.sub.10 = 0.85031 × 10.sup.-12               A.sub.11 = 0.0,                                                                            A.sub.12 = -0.57602 × 10.sup.-14,                                                    A.sub.13 = 0.0                                      A.sub.14 = -0.0,                                                                           A.sub.15 = 0.0,                                                                            A.sub.16 = 0.0                                    r.sub.6:                                                                        A.sub.2 = 0.0,                                                                             A.sub.3 = 0.0,                                                                             A.sub.4 = 0.87334 × 10.sup.-6                 A.sub.5 = 0.0,                                                                             A.sub.6 = 0.60545 × 10.sup.-8,                                                       A.sub.7 = 0.0                                       A.sub.8 = -0.53445 × 10.sup.-10,                                                     A.sub.9 = 0.0,                                                                             A.sub.10 = 0.93621 × 10.sup.-15               A.sub.11 = 0.0,                                                                            A.sub.12 = 0.29506 × 10.sup.-16,                                                     A.sub.13 = 0.0                                      A.sub.14 = -0.73084 × 10.sup.-18,                                                    A.sub.15 = 0.0,                                                                            A.sub.16 = 0.0                                    __________________________________________________________________________

As described above, a lens system for use in a copying machine includesonly three lens elements, one of which is formed of plastic to realizesubstantial reductions in cost as well as in weight. In conventionalfour component lens systems, the total lens thickness has a minimumvalue of 0.2f.

This invention provides a lens system with a greatly reduced thicknessof 0.1f to 0.21f, thereby allowing the entire copying machine to becompact. The lens system of this invention is comparable to or exceedsconventional lens systems in performance.

                                      TABLE 24                                    __________________________________________________________________________    f = 180    FNo. = 10.0                                                        __________________________________________________________________________    RADIUS OF CURV.                                                                          AXIAL DISTANCE                                                                           REFRACT. IND (Nd)                                                                         ABBE No. (νd)                            __________________________________________________________________________    r.sub.1                                                                           36.05                                                                                d.sub.1 7.70                                                                             N.sub.1 1.7856                                                                            ν.sub.1 42.8                             r.sub.2                                                                           119.23                                                                               d.sub.2 3.97                                                       r.sub.3                                                                           -878.47                                                                              d.sub.3 2.40                                                                             N.sub.2 1.5840                                                                            ν.sub.2 31.0                              r.sub.4 *                                                                        30.32                                                                                 d.sub.4 13.19                                                     r.sub.5                                                                           143.29                                                                               d.sub.5 5.39                                                                             N.sub.3 1.4914                                                                            ν.sub.3 57.8                              r.sub.6*                                                                         -123.71                                                                              Σd = 32.65                                                   __________________________________________________________________________    ASPHERICAL SURFACE COEFFICIENT                                                __________________________________________________________________________    r.sub.4 :                                                                       A.sub.2 = 0.0,                                                                             A.sub.3 = 0.0,                                                                             A.sub.4 = 0.20928 × 10.sup.-8                 A.sub.5 = 0.0,                                                                             A.sub.6 = 0.13288 × 10.sup.-11,                                                      A.sub.7 = 0.0                                       A.sub.8 = 0.16613 × 10.sup.- 13,                                                     A.sub.9 = 0.0,                                                                             A.sub.10 = 0.11863 × 10.sup.-13               A.sub.11 = 0.0,                                                                            A.sub.12 = -0.46941 × 10.sup.-15,                                                    A.sub.13 = 0.0                                      A.sub.14 = -0.0                                                                            A.sub.15 = 0.0,                                                                            A.sub.16 = 0.0                                    r.sub.6:                                                                        A.sub.2 = 0.0,                                                                             A.sub.3 = 0.0,                                                                             A.sub.4 = 0.88431 × 10.sup.-6                 A.sub.5 = 0.0,                                                                             A.sub.6 = 0.14548 × 10.sup.-7,                                                       A.sub.7 = 0.0                                       A.sub.8 = -0.84638 × 10.sup.-10,                                                     A.sub.9 = 0.0,                                                                             A.sub.10 = 0.36374 × 10.sup.-15               A.sub.11 = 0.0,                                                                            A.sub.12 = 0.11274 × 10.sup.-16,                                                     A.sub.13 = 0.0                                      A.sub.14 = 0.34066 × 10.sup.-18,                                                     A.sub.15 = 0.0,                                                                            A.sub.16 = 0.0                                    __________________________________________________________________________

                  TABLE 25                                                        ______________________________________                                                    [20]           [21]                                                           0.005f < d.sub.2 < 0.025f                                                                    0.05f < d.sub.4 < 0.08f                            ______________________________________                                        EMBODIMENT 17                                                                             0.0111f        0.0674f                                            EMBODIMENT 18                                                                             0.0111f        0.0674f                                            EMBODIMENT 19                                                                             0.0219f        0.0737f                                            EMBODIMENT 20                                                                             0.0221f        0.0733f                                            ______________________________________                                                    [22]                 [24]                                                     1.75 <    [23]       -0.1 < r.sub.4 /r.sub.5 <                                N.sub.1 < 1.85                                                                          35 < ν.sub.1 < 50                                                                     0.25                                         ______________________________________                                        EMBODIMENT 17                                                                             1.7620    40.4       0.0065                                       EMBODIMENT 18                                                                             1.7520    40.4       -0.0518                                      EMBODIMENT 19                                                                             1.8050    41.0       0.1421                                       EMBODIMENT 20                                                                             1.7856    42.8       0.2116                                       ______________________________________                                                    0.03f < f.sub.1 + f.sub.2 < 0.01f                                                            Σd                                           ______________________________________                                        EMBODIMENT 17                                                                             0.0530f        0.154f                                             EMBODIMENT 18                                                                             0.0562f        0.157f                                             EMBODIMENT 19                                                                             0.0773f        0.180f                                             EMBODIMENT 20                                                                             0.0726f        0.181f                                             ______________________________________                                    

The foregoing embodiments have been described in relation to aberrationsoccurring at -1x, i.e. real-size copying. In real-size copying, anaberration occurs in exactly the same amount, disregarding the sign ofdistortion, when an object plane and an image plane are interchanged.Thus, in the lens systems according to this invention, the elementopposed to the object plane and that opposed to the image plane may bereversed.

Although the present invention has been fully described by way ofexamples with reference to the accompanying drawings, it is to be notedthat various changes and modifications will be apparent to those skilledin the art. Therefore, unless otherwise such changes and modificationsdepart from the scope of the present invention, they should be construedas being included therein.

What is claimed is:
 1. A three group, three component lens systemcomprising, in order from one side:a first, positive meniscus lensdefining a convex surface directed to an object plane; a second,biconcave lens, and a third, biconvex lens, at least one of the threelenses being formed of plastic, the lens system included within aphotocopier system having a fixed distance between the object plane andan image plane and requiring a clarity of image to correspond across animage having a fixed size in both the object and image planes, the lenssystem satisfying the following expressions:
 0. 1f<f₁ +f₂ <0.2f (a)where f is a focal length of the lens system, f₁ is a focal length ofsaid first lens, and f₂ is a focal length of said second lens:

    0.03f<d.sub.4 <0.05f                                       (b)

where d₄ is an axial distance between said second and third lenses;

    40<0.5 (ν.sub.1 +ν.sub.3)<50                         (c)

where ν₁ is Abbe number of a material forming said first lens, and ν₃ isAbbe number of a material forming said third lens;

    1.65<0.5 (N.sub.1 +N.sub.3)<1.75                           (d)

where N₁ is a refractive index at line d of a material forming saidfirst lens, and N₃ is a refractive index at line d of a material formingsaid third lens; and

    0.18<r.sub.4 /r.sub.5 <0.23                                (e)

where r₄ is a radius of curvature of a surface of said second lensopposed to said third lens, and r₅ is a radius of curvature of a surfaceof said third lens opposed to said second lens.
 2. A lens system asclaimed in claim 1, wherein said second lens has an aspherical surface.3. A three group, three component lens system comprising, in order fromone side:a first, positive meniscus lens defining a convex surfacedirected to an object plane; a second, biconcave lens, and a third,biconvex lens, at least one of the three lenses being formed of plastic,the lens system included within a photocopier system having a fixeddistance between the object plane and an image plane and requiring aclarity of image to correspond across an image having a fixed size inboth the object and image planes, the lens system satisfying thefollowing expressions:

    40<0.5 (ν.sub.1 +ν.sub.3)<50                         (a)

where ν₁ is Abbe number of a material forming said first lens, and ν₃ isAbbe number of a material forming said third lens;

    0.04f<f.sub.1 +f.sub.2 <0.20f                              (b)

where f is a focal length of the entire lens system, f₁ is a focallength of said first lens, and f₂ is a focal length of said second lens;

    0.05f<d.sub.4 <0.08f                                       (c)

where d₄ is an axial distance between said second and third lenses, and

    0.10<r.sub.4 /r.sub.5 <0.25                                (d)

where r₄ is a radius of curvature of a surface of said second lensopposed to said third lens, and r₅ is a radius of curvature of a surfaceof said third lens opposed to said second lens.
 4. A three group, threecomponent lens system comprising, in order from one side:a first,positive meniscus lens defining a convex surface directed to an objectplane; a second lens having a negative power, and a third lens having apositive power, said second and third lenses being formed of plastic,and the lens system included within a photocopier system having a fixeddistance between the object plane and an image plane and requiring aclarity of image to correspond across an image having a fixed size inboth the object and image planes, the lens system satisfying thefollowing expressions:

    0.04f<f.sub.1 +f.sub.2 <0.06f                              (a)

where f is a focal length of the lens system, f₁ is a focal length ofsaid first lens, and f₂ is a focal length of said second lens;

    0.015f<d.sub.2 <0.025f                                     (b)

where d₂ is an axial distance between said first and second lenses;

    0.05f<d.sub.4 <0.15f                                       (c)

where d₄ ia an axial distance between said second and third lenses;

    35<ν.sub.1 <50, and                                     (d)

    1.65<N.sub.1

where ν₁ is Abbe number of a material forming said first lens, and N₁ isa refractive index at line d of the material forming said first lens. 5.A three group, three component lens system comprising, in order from oneside:a first, positive meniscus lens defining a convex surface directedto an object plane; a second lens having a negative power, and a thirdlens having a positive power, said second and third lenses being formedof plastic, and the lens system included within a photocopier systemhaving a fixed distance between the object plane and an image plane andrequiring a clarity of image to correspond across an image having afixed size in both the object and image planes, the lens systemsatisfying the following expressions:

    0.015f<f.sub.1 +f.sub.2 <0.05f                             (a)

where f is a focal length of the lens system, f₁ is a focal length ofsaid first lens, and f₂ is a focal length of said second lens;

    0.005f<d.sub.2 <0.015f                                     (b)

where d₂ is an axial distance between said first and second lenses;

    0.05f<d.sub.4 <0.15f                                       (c)

where d₄ is an axial distance between said second and third lenses;

    35<ν.sub.1 <50, and                                     (d)

    1.65<N.sub.1

where ν₁ is Abbe number of a material forming said first lens, and N₁ isa refractive index at line d of the material forming said first lens. 6.A lens system as claimed in claim 5, wherein said second and thirdlenses have at least one spherical surface.
 7. A three group, threecomponent lens system comprising, in order from one side:a first,positive meniscus lens defining a convex surface directed to an objectplane; a second lens having a negative power, and a third lens having apositive power, said second and third lenses being formed of plastic,and the lens system included within a compact photocopier system havinga fixed distance between the object plane and an image plane andrequiring a clarity of image to correspond across an image having afixed size in both the object and image planes, the lens systemsatisfying the following expressions:
 0. 005f<d₂ <0.025f (a) where f isa focal length of the lens system, and d₂ is an axial distance betweensaid first and second lenses;

    0.05f<d.sub.4 <0.08f                                       (b)

where d₄ is an axial distance between said second and third lenses;

    35<ν.sub.1 <50, and                                     (c)

    1.75<N.sub.1 <1.85

where ν₁ is Abbe number of a material forming said first lens, and N₁ isa refractive index at line d of the material forming said first lens;

    -0.1<r.sub.4 /r.sub.5 <0.25                                (d)

where r₄ is a radius of curvature of a surface of said second lensopposed to said third lens, and r₅ is a radius of curvature of a surfaceof said third lens opposed to said second lens.
 8. A lens system asclaimed in claim 7, wherein said second and third lenses have twoaspherical surfaces.